Problem: What do the following two equations represent? $x+y = 3$ $-5x+5y = -1$
Explanation: Putting the first equation in $y = mx + b$ form gives: $x+y = 3$ $y = -x+3$ Putting the second equation in $y = mx + b$ form gives: $-5x+5y = -1$ $5y = 5x-1$ $y = 1x - \dfrac{1}{5}$ The slopes are negative inverses of each other, so the lines are perpendicular.